Proinov contractions and discontinuity at fixed point

Ravindra K. Bisht; R. P. Pant; Vladimir Rakočević

doi:10.18514/MMN.2019.2277

Proinov contractions and discontinuity at fixed point

Ravindra K. Bisht, R. P. Pant, Vladimir Rakočević

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245.

Original language	English
Pages (from-to)	131-137
Number of pages	7
Journal	Miskolc Mathematical Notes
Volume	20
Issue number	1
DOIs	https://doi.org/10.18514/MMN.2019.2277
Publication status	Published - 2019
Externally published	Yes

Keywords

(∈-δ) contractions
Fixed point
Orbital continuity
Power contraction

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Numerical Analysis
Discrete Mathematics and Combinatorics
Control and Optimization

Access to Document

10.18514/MMN.2019.2277

Cite this

@article{9880cd8352734b4889154ca99ebd449d,

title = "Proinov contractions and discontinuity at fixed point",

abstract = "In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245.",

keywords = "(∈-δ) contractions, Fixed point, Orbital continuity, Power contraction",

author = "Bisht, {Ravindra K.} and Pant, {R. P.} and Vladimir Rako{\v c}evi{\'c}",

note = "Publisher Copyright: {\textcopyright} 2019 Miskolc University Press.",

year = "2019",

doi = "10.18514/MMN.2019.2277",

language = "English",

volume = "20",

pages = "131--137",

journal = "Miskolc Mathematical Notes",

issn = "1787-2405",

publisher = "Miskolc University Press",

number = "1",

}

TY - JOUR

T1 - Proinov contractions and discontinuity at fixed point

AU - Bisht, Ravindra K.

AU - Pant, R. P.

AU - Rakočević, Vladimir

PY - 2019

Y1 - 2019

N2 - In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245.

AB - In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245.

KW - (∈-δ) contractions

KW - Fixed point

KW - Orbital continuity

KW - Power contraction

UR - http://www.scopus.com/inward/record.url?scp=85067464843&partnerID=8YFLogxK

U2 - 10.18514/MMN.2019.2277

DO - 10.18514/MMN.2019.2277

M3 - Article

AN - SCOPUS:85067464843

SN - 1787-2405

VL - 20

SP - 131

EP - 137

JO - Miskolc Mathematical Notes

JF - Miskolc Mathematical Notes

IS - 1

ER -

Proinov contractions and discontinuity at fixed point

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this